Potter Cervantes
10/04/2023 · Elementary School
Graph the linear function by finding \( x \) - and \( y \)-intercepts. Then write the equation using function notation. \[ x-y=-3 \]
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Tutor-Verified Answer
Step-by-step Solution
To graph the linear function given by the equation \( x - y = -3 \), we can find the \( x \)- and \( y \)-intercepts.
### Step 1: Find the \( x \)-intercept
The \( x \)-intercept occurs when \( y = 0 \). We can find it by substituting \( y = 0 \) into the equation:
\[
x - 0 = -3 \implies x = -3
\]
So, the \( x \)-intercept is \( (-3, 0) \).
### Step 2: Find the \( y \)-intercept
The \( y \)-intercept occurs when \( x = 0 \). We can find it by substituting \( x = 0 \) into the equation:
\[
0 - y = -3 \implies -y = -3 \implies y = 3
\]
So, the \( y \)-intercept is \( (0, 3) \).
### Step 3: Plot the intercepts
Now we can plot the points \( (-3, 0) \) and \( (0, 3) \) on a coordinate plane.
### Step 4: Draw the line
Draw a straight line through the points \( (-3, 0) \) and \( (0, 3) \). This line represents the linear function.
### Step 5: Write the equation in function notation
To express the equation in function notation, we can solve for \( y \):
Starting from the original equation:
\[
x - y = -3
\]
Rearranging gives:
\[
-y = -x - 3
\]
Multiplying through by -1:
\[
y = x + 3
\]
Thus, in function notation, we can write:
\[
f(x) = x + 3
\]
### Summary
- The \( x \)-intercept is \( (-3, 0) \).
- The \( y \)-intercept is \( (0, 3) \).
- The equation in function notation is \( f(x) = x + 3 \).
Quick Answer
The \( x \)-intercept is \( (-3, 0) \), the \( y \)-intercept is \( (0, 3) \), and the function notation is \( f(x) = x + 3 \).
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